**3. Thermophysical properties of nanofluid**

In this study, it simulated the core of the VVER-1000 reactor with solid and annular fuel using *Al*2*O*<sup>3</sup> nanofluid as coolant. **Table 3** shows the physical and thermal properties of this nanoparticle and base fluid [29].

The correlations for density (*ρnf* ), specific heat *Cpnf* , viscosity (*μnf* ), and thermal conductivity (*knf* ) of the nanofluid can be obtained [28, 30, 31]:

$$
\rho\_{\rm nf} = (\mathbf{1} - \mathbf{q})\rho\_{\rm nf} + \mathbf{q}\rho\_{\rm bf} \tag{4}
$$

$$\mathbf{Cp\_{nf}} = (\mathbf{1} - \mathfrak{q})\mathbf{Cp\_{bf}} + \mathfrak{q}\mathbf{Cp\_{bf}} \tag{5}$$

$$
\mu\_{\rm nf}/\mu\_{\rm bf} = \mathbf{123q}^2 + \mathbf{7.3q} + \mathbf{1} \tag{6}
$$


**Table 3.**

*Thermo-physical properties of nanoparticles and base fluids [16].*

$$k\_{\rm nf}/k\_{\rm bf} = 4.97\rho^2 + 2.72\rho + 1\tag{7}$$

In this simulation, *φ* is the volume fraction of nanofluid considered 5,10, 20.

*ρbf* , *Cpbf* , *μbf* , and *kbf* are density, specific heat, viscosity, and thermal conductivity of the pure fluid, respectively.
